Understanding the Unit of θ in the Equation ΔT = Pθ

In summary, the equation ΔT = Pθ relates temperature difference (ΔT) to power (P) and a constant value (θ). The unit of θ can be found using dimensional analysis, and it is equal to m^2 kg / s^3. This unit is derived from the units of force, time, and distance in Joules. The value of θ can be determined by finding an equation that relates it to physical constants and variables.
  • #1
fran1942
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Homework Statement


In the equation ΔT = Pθ, P is power in Joules per second and ΔT is the temperature difference in °C. Use dimensional analysis to find the unit of θ. Hint, Joules has units of Force time distance.

My question is: I don't understand what they mean by finding the unit of θ. Are they saying that P needs to be multiplied by θ, or does θ simply represent the unit of P that I have worked out below ?
Sorry, I am unfamiliar with how Physics questions are worded.

The Attempt at a Solution


I am pretty sure the answer is m^2 kg / s^3
If correct, how does my answer relate to θ ?
 
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  • #2
This expression is the first law of thermo. See if you can find an equation for theta based on physical constants and variables and I think it will make sense.
 
  • #3
thanks, so is my answer of m^2 kg / s^3 not correct ?
 

Related to Understanding the Unit of θ in the Equation ΔT = Pθ

1. What is the unit for theta?

The unit for theta is radians (rad) when used to measure angles in trigonometry, physics, and other mathematical fields. However, theta can also represent other quantities such as temperature or time, in which case the unit would depend on the specific context.

2. How do you find the unit of theta?

The unit of theta can be found by looking at the given context or equation in which it is used. If it represents an angle, then it is usually specified as radians, degrees, or another angular unit. If it represents a physical quantity, then the unit can be derived from the equation or measurement.

3. Can theta have different units?

Yes, theta can have different units depending on how it is used. As mentioned before, it can represent angles or other quantities, each with their own set of units. For example, theta can also represent temperature in degrees Celsius or time in seconds.

4. Why is theta often measured in radians?

Theta is often measured in radians because it simplifies many mathematical equations and makes them more elegant. Radians are also a more natural unit for measuring angles, as they are based on the radius of a circle rather than arbitrary divisions like degrees.

5. How can I convert theta from one unit to another?

To convert theta from one unit to another, you can use conversion formulas specific to the units involved. For example, to convert theta from degrees to radians, you can use the formula radians = degrees * pi/180. Alternatively, there are also online conversion tools available for quick and accurate conversions.

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